For linear elastic frame, if stiffness matrix is doubled with respect to the existing stiffness matrix, the deflection of the resulting frame will be

For the plane frame with an overhang as shown below, assuming negligible axial deformation, the degree of static indeterminacy, $$d,$$ and the degree of kinematic indeterminacy, $$k,$$ are

A homogeneous, simply supported prismatic beam of width $$B,$$ depth $$D$$ and span $$L$$ is subjected to a concentrated load of magnitude $$P.$$ The load can be placed anywhere along the span of the beam. The maximum flexural stress developed in beam is

The star and grid pattern of road networks are adopted in